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Applicable Mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. History Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed, to include representations, asymptotic methods, variation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vehicle Routing Problem Example
A vehicle (from la, vehiculum) is a machine that transports people or cargo. Vehicles include wagons, bicycles, motor vehicles (motorcycles, cars, trucks, buses, mobility scooters for disabled people), railed vehicles (trains, trams), watercraft (ships, boats, underwater vehicles), amphibious vehicles (screw-propelled vehicles, hovercraft), aircraft (airplanes, helicopters, aerostats) and spacecraft.Halsey, William D. (Editorial Director): ''MacMillan Contemporary Dictionary'', page 1106. Macmillan Publishers, MacMillan Publishing, 1979. Land vehicles are classified broadly by what is used to apply steering and drive force (physics), forces against the ground: wheeled vehicle, wheeled, tracked vehicle, tracked, railed vehicle, railed or Ski#Use on vehicles, skied. ISO 3833-1977 is the standard, also internationally used in legislation, for road vehicles types, terms and definitions. History * The oldest boats found by archaeological excavation are logboats, with the ol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation (mathematics)
In mathematics, a representation is a very general relationship that expresses similarities (or equivalences) between mathematical objects or structures. Roughly speaking, a collection ''Y'' of mathematical objects may be said to ''represent'' another collection ''X'' of objects, provided that the properties and relationships existing among the representing objects ''yi'' conform, in some consistent way, to those existing among the corresponding represented objects ''xi''. More specifically, given a set ''Π'' of properties and relations, a ''Π''-representation of some structure ''X'' is a structure ''Y'' that is the image of ''X'' under a homomorphism that preserves ''Π''. The label ''representation'' is sometimes also applied to the homomorphism itself (such as group homomorphism in group theory). Representation theory Perhaps the most well-developed example of this general notion is the subfield of abstract algebra called representation theory, which studies the representing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Population Models
Matrix population models are a specific type of population model that uses matrix algebra. Population models are used in population ecology to model the dynamics of wildlife or human populations. Matrix algebra, in turn, is simply a form of algebraic shorthand for summarizing a larger number of often repetitious and tedious algebraic computations. All populations can be modeled :N_=N_+B-D+I-E, where: *Nt+1 = abundance at time t+1 *Nt = abundance at time t *B = number of births within the population between Nt and Nt+1 *D = number of deaths within the population between Nt and Nt+1 *I = number of individuals immigrating into the population between Nt and Nt+1 *E = number of individuals emigrating from the population between Nt and Nt+1 This equation is called a BIDE model (Birth, Immigration, Death, Emigration model). Although BIDE models are conceptually simple, reliable estimates of the 5 variables contained therein (N, B, D, I and E) are often difficult to obtain. Usually a re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biologist
A biologist is a scientist who conducts research in biology. Biologists are interested in studying life on Earth, whether it is an individual cell, a multicellular organism, or a community of interacting populations. They usually specialize in a particular branch (e.g., molecular biology, zoology, and evolutionary biology) of biology and have a specific research focus (e.g., studying malaria or cancer). Biologists who are involved in basic research have the aim of advancing knowledge about the natural world. They conduct their research using the scientific method, which is an empirical method for testing hypotheses. Their discoveries may have applications for some specific purpose such as in biotechnology, which has the goal of developing medically useful products for humans. In modern times, most biologists have one or more academic degrees such as a bachelor's degree plus an advanced degree like a master's degree or a doctorate. Like other scientists, biologists can be fou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others. Core concepts related to information security ( data confidentiality, data integrity, authentication, and non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications. Cryptography prior to the modern age was effectively synonymo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of Complex analysis, analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Engineering
Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specialized List of engineering branches, fields of engineering, each with a more specific emphasis on particular areas of applied mathematics, applied science, and types of application. See glossary of engineering. The term ''engineering'' is derived from the Latin ''ingenium'', meaning "cleverness" and ''ingeniare'', meaning "to contrive, devise". Definition The American Engineers' Council for Professional Development (ECPD, the predecessor of Accreditation Board for Engineering and Technology, ABET) has defined "engineering" as: The creative application of scientific principles to design or develop structures, machines, apparatus, or manufacturing processes, or works utilizing them singly or in combination; or to construct o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Mechanics
Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and biomedical engineering, geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion. It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms; that is, it models matter from a ''macroscopic'' viewpoint rather than from ''microscopic''. Fluid mechanics, especially fluid dynamics, is an active field of research, typically mathematically complex. Many problems are partly or wholly unsolved and are best addressed by numerical methods, typically using computers. A modern discipline, called computational fluid dynamics (CFD), is dev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility). The earliest development of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on foundational works of Sir Isaac Newton, and the mathematical methods invented by Gottfried Wilhelm Leibniz, Joseph-Louis Lagrange, Leonhard Euler, and other contemporaries, in the 17th century to describe the motion of bodies under the influence of a system of forces. Later, more abstract methods were developed, leading to the reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances, ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newtonian Physics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility). The earliest development of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on foundational works of Sir Isaac Newton, and the mathematical methods invented by Gottfried Wilhelm Leibniz, Joseph-Louis Lagrange, Leonhard Euler, and other contemporaries, in the 17th century to describe the motion of bodies under the influence of a system of forces. Later, more abstract methods were developed, leading to the reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances, made predo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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